A cell of internal resistance r drives current through an external resistance R . The power delivered by the cell to the external resistance will be maximum when:

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Current i = E r + R Power generated in R P = i 2 R P = E 2 R ( r + R ) 2 for maximum power d P d R = 0 E 2 ( r + R ) 2 × 1 - R × 2 ( r + R ) ( r + R ) 4 = 0 ⇒ when, r = R then, d P d R = 0

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